Non-BCS superfluidity in trapped ultracold Fermi gases

TL;DR

This paper investigates exotic superfluid phases in polarized ultracold Fermi gases trapped in potential wells, revealing shell structures and density features that differ from traditional BCS superfluidity, using Bogoliubov-de Gennes equations.

Contribution

It demonstrates the emergence of non-BCS superfluid phases as shell structures in trapped gases due to polarization, using a detailed microscopic approach.

Findings

Exotic superfluid shells form around the BCS core in polarized gases.

Large polarization leads to superfluidity in the core as well.

Density difference exhibits a small dip at the trap center in polarized superfluids.

Abstract

Superconductivity and superfluidity of fermions require, within the BCS theory, matching of the Fermi energies of the two interacting Fermion species. Difference in the number densities of the two species leads either to a normal state, to phase separation, or - potentially - to exotic forms of superfluidity such as FFLO-state, Sarma state or breached pair state. We consider ultracold Fermi gases with polarization, i.e. spin-density imbalance. We show that, due to the gases being trapped and isolated from the environment in terms of particle exchange, exotic forms of superfluidity appear as a shell around the BCS-superfluid core of the gas and, for large density imbalance, in the core as well. We obtain these results by describing the effect of the trapping potential by using the Bogoliubov-de Gennes equations. For comparison to experiments, we calculate also the condensate fraction, and show that, in the center of the trap, a polarized superfluid leads to a small dip in the central density difference. We compare the results to those given by local density approximation and find qualitatively different behavior.